Equivalence & Bi-implication
- The Converse of Statement
- Equivalent Statements
The Converse of Statement:
Let A → B be an implication, then the converse of A → B is B → A
Let the implication X → Y be true, if Y → X is true, then X and Y are said to be equivalent statements. Thus, we write and say that X ↔ Y is a bi-implication.
Given the statements:
P1: The teacher entered and started the lesson
P2: Either it will rain tomorrow or the visit will take place, or it will rain tomorrow and the visit will take place anyway.
Use appropriate symbols and truth tables to describe:
1. The conditions for P1 to be true,
2. The conditions under which P2 will be false
1. Let the sub-statements be
A: the teacher entered
B: the teacher started the lesson
If P1 is true, then A → B is true.
Recall, the relation “and” which suggests both A and B must true before A → B could be true
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